Bluebook SAT Test Bluebook SAT Math: Advanced Functions Questions and Answers 3

Question 1

The function f(x) = (x - 1)(x + 3) has x-intercepts at:

Accepted Answer

x = 1 and x = -3

Answer

Setting each factor to zero: x - 1 = 0 gives x = 1, and x + 3 = 0 gives x = -3.

Question 2

If f(x) = √(x + 4), what is the domain of f?

Accepted Answer

x ≥ -4

Answer

The radicand must be non-negative: x + 4 ≥ 0, so x ≥ -4.

Question 3

A function f satisfies f(2) = 5 and f(5) = 11. If f is linear, what is f(8)?

Accepted Answer

17

Answer

The slope is (11-5)/(5-2) = 2, so each step of 3 adds 6; f(8) = 11 + 6 = 17.

Question 4

If g(x) = x² + bx + c has a vertex at (3, -4), what is the value of b?

Accepted Answer

-6

Answer

The vertex x-coordinate is -b/(2a) = 3, so -b/2 = 3, giving b = -6.

Question 5

For f(x) = |x - 2| + 1, which statement is true?

Accepted Answer

The minimum value of f is 1

Answer

Since |x - 2| ≥ 0, the minimum occurs when |x - 2| = 0 (at x = 2), giving f(2) = 1.

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